The Napier’s Bones is a mathematical tool that dates back to the 17th century. Invented by the Scottish mathematician John Napier, it’s a clever set of rectangular rods nestled in a frame, each divided into multiple squares. These strips, also named “bones,” were designed to simplify complex multiplication and division problems, making mathematical calculations more accessible and efficient.
The Napier’s Bones set is the second mathematical tool from John Napier that we designed and are manufacturing. In a previous post, we explained the use of Napier’s Local Arithmetic Board, which is the precursor to modern digital computing, as it uses the same binary logic. In this post, we will explore how multiplication and division with one or two digits can be done using Napier’s Bones, which is similar to the principles of lattice multiplication.
Materials
Related materials: Napier’s Local Arithmetic Board Complete Set, Napier’s Local Arithmetic Board (Task Cards), Napier’s Local Arithmetic Board
Multiplying Using 1-digit Multipliers (Task Cards – NB1)
Multiplying with Napier’s Bones is learning to see logical and repetitive patterns in math! Multiplying large numbers with a 1-digit multiplier is very simple. For example, 9674 x 8 = … Build the multiplicand (9674) using the bones (strips). Then, look at the row labeled “8” on the left side. You will notice squares made of triangles labeled with numbers. Add numbers that are together diagonally (see pictures). Each sum is part of the final product of your multiplication. Of course, numbers adding up to 10 must be carried over.
Multiplying Using 2-digit Multipliers (Task Cards – NB2)
Multiplying numbers with a 2-digit multiplier is similar to the example above. However, because your learners will need to read rows of numbers and add them diagonally, we provided you with reproducible grids to copy. That way, your learners can join the rows and read the final product more easily. Examine the example provided in the pictures: 8364 x 24. Copy the numbers in rows 2 and 4 on the template from the Napier’s Bones frame. Then, add the numbers diagonally to find the final product! Our lesson plan offers an alternate method to multiplying with 2 digits.
Dividing Using 1-digit Divisors (Task Cards – NB3)
The Napier’s Bones act as a matrix with multiples of numbers 1-9. Therefore, it is easy to use it for divisions. For example, in the division 364 / 7, 364 is the dividend, and 7 is the divisor. Take strip 7 (the divisor) from the Napier’s Bones frame. The strip provides all the multiples 7 (7, 14, 21, 28, 35, 42, 29, 56, 63). Ask your learners how many times 7 goes into [36] (from the dividend 364). They will have to look for the largest number that does not exceed “36,” which is 35. Look at the corresponding number that appears on the left side of the frame (5). Write this number as part of the quotient above the line. Continue using the same process used for solving a division.
Dividing Using 2-digit Divisors (Task Cards – NB4)
The same process is used to solve 2-digit divisions. The divisors are taken from the bones. Additional printed strips are included for learners to build potential divisors with double digits (55, 333). A whiteboard or paper can be used to record the multiples and keep track of calculations. You will find more information in our instructional guide!
We hope you enjoyed learning about our revamped version of the Napier’s Bones! We believe children should experience various ways to compute in order to refine their mathematical minds! For more math materials, visit our website at www.alisonsmontessori.com.
